band pass fss

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©2009 Sonnet Software, Inc. (315)453-3096 [email protected] 1 Double Seivenpiper FSS with Plane Wave Radiation On and Off Normal Simulation Using CST Studio Suite Microwave Studio ® at Sonnet Software, Inc. Dr. James R Willhite

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Double Seivenpiper FSS with Plane Wave Radiation On and Off Normal

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Page 1: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

1

Double Seivenpiper FSS with Plane Wave Radiation On and Off Normal

Simulation Using CST Studio Suite

Microwave Studio® at Sonnet Software, Inc.Dr. James R Willhite

Page 2: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Frequency Selective SurfaceThis is a study of a frequency selective surface (FSS) built as 2 back-to-back Seivenpipersurfaces. The figure to the left shows a unit cell of the infinite array.

The FSS was initially designed for a normally incident plane wave in Microwave Studio using the time domain (transient) solver because of the speed of such simulations. The surface was then studied using the frequency domain solver for off-normal beams.

Unit cell is 5x5x3.3mm for a 6 GHz FSS

Page 3: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Cross Section of FSSThe FSS was built as back-to-back Seivenpiper arrays. There is a dielectric stack-up with square metal plates and vias. On either side of the FSS there are floating plates which are the top plates of capacitors. Inside are plates serving as the bottom plate of the capacitor. These bottom plates are shifted to have their centers on the edge of the unit cell and therefore to couple the top plates of adjacent cells. The bottom plates for the left half were rotate 45 . Both of these layers (left and right) are connected to a central “ground” plate by vias. The via posts act as inductors and the ground plate gives a return path between the bottom plates.

top plates

bottom plates

“ground” plate

inductive via posts

Page 4: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Symmetry & BoundariesThe model was built with geometric symmetry; mirror planes at both x-z and y-z. If these are used with electric and magnetic boundaries to the workspace, the model size is reduced to ¼-th the original. A high quality simulation of the transmission through this FSS can then be done in less than 8 minutes with a rather slow, 5 year old desktop and requires less than 80M of RAM using the transient solver in MWS. This then was the technique chosen for the initial optimization.

Page 5: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Model Parameters

The FSS was built with parameters controlling the geometry. These were used to optimize the structure for the transmission characteristics we desired.

Page 6: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Plane Wave Excitation

Ports were placed at the zmin and zmax boundaries of the workspace and with the boundaries shown previously the port modes are TEM; one polarization of plane wave. By doing a standard S-parameter simulation we get the transmission of this wave.

Page 7: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Port Signals

A sharp Gaussian pulse of the TEM mode of the port was applied in the time domain (orange signal) and the reflection and transmission monitored (oscillatory signals).

Page 8: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Scattering Parameters of FSS

After adjusting the parameters of the model, the results shown above were obtained: a transmission pass band centered near 6GHz.

transmission

reflection

Page 9: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Boundaries for Frequency Domain SolverBecause periodic boundaries with non-zero phase shift have not been developed for time domain simulations, simulation of an infinite array in the time domain is limited to a normally incident beam. To study radiation coming in at an angle we must use the frequency domain solver.

Page 10: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Phase for Unit Cell Boundaries

The boundaries for unit cells can be set to have non-zero phase shifts. These point the beam off the normal to the FSS surface. We used parameters to define the beam direction.

Page 11: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Floquet Mode BoundaryIn the frequency domain solver for MWS, if unit cell boundaries are placed on an array (x and y boundaries) any open boundary in z becomes a Floquet port. These are highly efficient at absorbing radiation even coming far off normal.

The Floquet ports have modes similar to waveguides. By default CST places 18 modes at each port and these modes absorb (and excite) radiation leaving the surface of the array. We can again get the transmission properties of the FSS but now off normal if desired. The lowest 2 modes will be the 2 linear polarizations of the plane wave.

Page 12: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Adapted Tetrahedral Mesh

During the initial phase of a simulation using the frequency domain solver, the tetrahedral mesh is adapted until the S-parameters have converged at a set frequency. This shows the adapted mesh for the double Seivenpiper surface.

Page 13: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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S-Parameters at Normal IncidenceUsing the frequency domain solver we can see the results for both linear polarizations of the incident plane wave.

At 6GHz, the transmission through the FSS is -1.43dB and the reflection is -6.2dB.

Because of the symmetry of the geometry and the incident plane wave there should be no coupling of one polarization to the other. The coupling values of -50dB at 6GHz show the noise floor of the calculation at that frequency.

This simulation required 3 hours with the frequency domain solver compared with 8 minutes for the time domain solver

Page 14: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Attenuation of Higher Order Modes at Normal Incidence

With the phase of the boundary set for a normal incidence, the higher order Floquet modes are attenuated and group into a few sets with similar transmission characteristics.

Page 15: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Higher Order Modes at φ = 0 and θ = 60

If the boundary phases are scanned away from zero, the attenuation of the higher order Floquet modes changes. If the attenuation drops to zero for a set of modes, these become grating lobes for the array, usually something to avoid.

Page 16: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Transmission vs. Beam Direction in H-plane

The incident beam direction was scanned away from normal and the transmission characteristics recorded. This shows the transmission as the beam is scanned in the H-plane. The pass band moves up in frequency and the “valley” becomes deeper.

Page 17: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Transmission vs. Beam Direction in E-plane

This figure shows the transmission as the beam is scanned in the E-plane. The change is transmission is less than with the other scanner direction.

Page 18: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Mean Transmission from 5.5 to 6.5 GHz

H-plane E-plane

These figures show the mean transmission (linear) over the band 5.5 to 6.5 GHz as the beam is scanned off normal. The H-plane scan rolls off from 0.87 at normal to 0.66 at 60 . For the E-plane scan the change is much less. The mean transmission stays above 0.85 over the entire scan.

Page 19: Band Pass Fss

©2009 Sonnet Software, Inc. (315)453-3096 [email protected]

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Summary• Microwave Studio is well suited to design and

study the transmission characteristics of FSS as infinite arrays using either the time domain solver or the frequency domain solver.

• The transient solver can be used for rapid simulations and optimization. It is limited to normal incidence of the beam.

• The frequency domain solver can be used to study beams off the normal to the array using Floquet mode ports.